QCD factorization for the four-body leptonic B-meson decays

A bstract Employing the QCD factorization formalism we compute $$ {B}_u^{-}\to {\gamma}^{\ast}\mathrm{\ell}{\overline{v}}_{\mathrm{\ell}} B u − → γ ∗ ℓ v ¯ form factors with an off-shell photon state possessing virtuality of order m b Λ and {m}_b^2 m b 2 , respectively, at next-to-leading in QCD. Perturbative resummation for enhanced logarithms /Λ resulting formulae is subsequently accomplished logarithmic accuracy renormalization-group technique momentum space. In particular, derive soft-collinear a variety subleading power corrections to exclusive radiative {\gamma}^{\ast }{W}^{\ast } W hard-collinear \mathcal{O}\left({\alpha}_s^0\right) O α s 0 . We further construct complete set angular observables governing full differential distribution four-body leptonic decays {\mathrm{\ell}}^{\prime }{\overline{\mathrm{\ell}}}^{\prime}\mathrm{\ell}{\overline{v}}_{\mathrm{\ell}} ′ ℓ ℓ′ ∈ { e μ then perform exploratory phenomenological analysis number decay accessible LHCb Belle II experiments, emphasis on systematic uncertainties arising from shape parameters leading-twist B -meson light-cone amplitude heavy quark effective theory.